A charged particle carrying charge 1 μ C is moving with velocity (2 i +3 j +4 k ) ms^-1. If an external magnetic field of (5 i +3 j -6 k ) × 10^-3 T…

A charged particle carrying charge $\displaystyle 1 \mu \mathrm{C}$ is moving with velocity $\displaystyle (2 \hat{i}+3 \hat{j}+4 \hat{k})$ $\displaystyle \mathrm{ms}^{-1}$. If an external magnetic field of $\displaystyle (5 \hat{i}+3 \hat{j}-6 \hat{k}) \times 10^{-3} \mathrm{~T}$ exists in the region where the particle is moving then the force on the particle is $\displaystyle \overrightarrow{\mathrm{F}} \times 10^{-9} \mathrm{~N}$. The vector $\displaystyle \vec{F}$ is :